I wasn't clear : phase shift has a clear example: think of two sine waves, one whose value at time t is sin(t) and the other sin(t+pi/2). they'd have the same period, and frequency, but would be phase shifted by that addition in the time parameter.
For another fun example, here's the residential power in current American homes: two 120v A/C feeds, out of phase so that you can combine them in the breaker box to get 240v A/C.